Should the inability of our manager to utilize players correctly prevent us from signing players that are useful pieces?

You're not wrong, though....

You could make the argument that any time a team loses it is because a manager used his players incorrectly. Jim Leyland didn't make the World Series because he used his bullpen in the eighth inning of Game 2 of the ALCS when he had a starter the Red Sox found unhittable through seven. (Maybe there's a discussion thread somewhere insisting that's is why Leyland was forced to resign.) Bruce Bochy didn't just lose a game in 2012 (although he was forgiven because his team would sweep the Tigers in the World Series a few months later), but by putting Aubrey Huff at second base for the first time in his career, no one covered second on a play that could have ended the game with a win, and shortly thereafter Huff suffered a mental breakdown that pretty ended whatever career he had left. Any time a designated hitter goes a game without hitting the ball out of the infield, you could blame the manager for not utilizing him correctly.

On the other hand, teams that win frequently have players stepping up to do things out of their comfort zone. Often that's why they win. Often asking a player to do things fans in retrospect looking at their failure is the only chance a team has to win.

Complaining about a manager's inability to utilize players correctly is more tired than insightful.

I'm confident that anyone managing the White Sox (with the possible exception of Terry Bevington) has a better idea of how to use his roster to succeed more than fans do, regardless of how fashionable it might be to complain that Robin Ventura is a bad manager based on a hypothetical signing and a hypothetical use of the signed player.